I like using fleece as a back for quilts that I want to have a softer back i.e. the elderly, or babies which have more tender skin or if I want a lighter weight quilt. I don't use batting with fleece but I do when I use soft flannel for a backing.
As far as being faster I find using the pillowcase method to be faster. This method is done by putting right sides together,sewing around all edges but leaving a 3-4" opening in a seam to turn right side out. Trim corners and turn right side out. Press edges and hand stitch opening closed. Then quilt or tie the two layers together using whatever method you choose.

Yes it would. The instructions we had was to use batting in between...not a good idea as almost too much thickness. The suggestion given is much better. The fleece replaces a 2nd piece of cotton and the batting normally used.
If you are adding a pocket to fold it into as a quillow...that needs to be a 20 inch square sewn on the cotton's right side before adding the fleece.
Right side down on the fleece as you will be pulling it thru the opening.
Good luck...

Let me be sure you understand how I did mine as sometimes the directions in my head do not transfer to my fingers when typing.

I took a pieced top (or it could be a "cheater" top or a piece of fabric) the same size as my piece of (polar) fleece, the same type of fleece that's very popular now to make vests,jackets,etc. Usually the fleece is wider than I need so it has to be trimmed to fit the top part.
Then I put right sides together, pin, matching edges all around. Using a "walking foot or self feed foot" on my sewing machine I begin sewing 2/3 of the way down one side and proceed around all the sides until I come back to where I started leaving a 3"-4" opening to turn right side out. Trim seam allowance bulk at corners before turning. Turn right side out. Gently press edges flat. ( I use a pressing cloth & a bit of steam but not alot of pressure as it can leave the fleece "flat"). Stitch the turn opening closed. I usually do this by hand.
With the fabrics laying on a flat surface ,smooth out all wrinkles and safety pin "baste" the two layers together. At this point you can quilt it or tie it. I have tied mine using 2 strands of perle cotton thread-no knot to start. Beginning on the top side go down, leaving about a 2"-3" length of thread on top. Approx. 1/4" to the side of the thread on the back side,go back to the top. Repeat by going in same holes down and back up. Trim to the same length as other tail. Tie the "tails" together with the knot close to the fabric. Repeat this process every 4" or so. (Ties need to be close enough to hold the two layers together nicely.)Whatever you use to tie or quilt will still show on the back but the comforter/quilt will not be as heavy or thick as one using the batting. I use about 2 or 3 skeins of perle cotton to tie a 45" X47" comforter/quilt. I have never quilted one but I'm sure it would work fine as long as you used a "walking" foot

I think there may have been another thread on using fleece as a backing but I'm not sure.

I hope I explained my directions clearly but not in a childish manner. I work with elementary(PreK-5th grade) children all day and sometimes I forget how to talk in adult terms. :roll: